Study On The Relative Efficiency In Parameter Estimation For Linear Model

Linear model is one of the most important branches which develops earlier and concludes more theories in mathematical statistics.Linear model is an important statistic model which includes many statistical models for example linear regression model,variance analysis model , covariance analysis model and variance component model .Though the best linear unbiased estimate (BLUE) is the most perfect estimate of unknown parameters, it is difficult or impossible for us to get it for some reason. The least square estimate (LSE) is widely used as its minimalist covariance among estimates of the unbiased parameters. The loss is inevitable and sometimes this loss is great. To measure it,a lot of scholars put forward relative efficiencies of the least square estimate to the best linear unbiased estimate for the unknown parameter from different aspects.Some scholars discuss the relative efficiency and their corresponding nature linear model.The main results of this paper are listed in the following.â… .We elaborate the cause of the relative efficiency being and generalize the literature of internal and abroad in generalized linear model,growth curve model and linear weighted regression model in relative fields respectively. At the same time we introduce the 1atest development and the main results . What we have to study in this paper is also introduced.â…¡.A new relative efficiency which is first proposed in linear model in [1] is extended to generalized linear model . The lower bound is given and the relation with some generalized correlation coefficients is also discussed. Some useful results are got.â…¢.Three new relative efficiencies in other models are extended to general growth curve model. Their upper bounds are also studied.â…£.Firstly,a new relative efficiency in linear weighted regression model is proposed. The lower bound is given and the relation with some generalized correlation coefficients is also discussed. Then we get two new relative efficiencies about mean matrix and their upper bounds.